CN108983418A - A kind of free-form surface lens face type design method can be used for preparing hollow beam - Google Patents
A kind of free-form surface lens face type design method can be used for preparing hollow beam Download PDFInfo
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Abstract
The invention discloses a kind of free-form surface lens face type design methods that can be used for preparing hollow beam, belong to nonimaging optics technical field.Present system includes that freely bent lens and an optical focusing system are based on the law of refraction and law of conservation of energy and design the free form surface that can prepare hollow beam under the auxiliary of computer according to the deflection of light characteristic of Ideal Focusing System.Incident ray generates the hot spot that center intensity is zero after free form surface deviation and condenser lens convergence, in target illumination field.Present invention design guarantees that outer diameter size is controllable, peripheral even intensity while the Center Dark Spot size for realizing hot spot is controllable.In addition, the design can obtain the hollow beam (~10 μm) of micron dimension, there is important application in optical control and super-resolution imaging field.The present invention designs the continuity that can guarantee curved surface, easy to process.
Description
Technical field
The present invention relates to nonimaging optics and lighting technical field more particularly to a kind of it can be used for preparing hollow beam
Free-form surface lens face type design method.
Background technique
One free form surface of design is required to realize scheduled match according to the intensity distribution of light source (laser) and target illumination
Light requirement, this is a reverse engineer problem, is always the hot and difficult issue of nonimaging optics research.Since free form surface has spirit
The advantages that space layout living and design freedom, can not only greatly simplify the structure of optical system using free form surface, may be used also
Easily realize complicated lighting requirement.
Currently, generalling use optimization design and " Partial Differential Equation (PDE) " method to design
Free form surface is to solve the problems, such as the reverse illumination.Optimization design by certain optimization algorithm, by constantly change optimized variable come
Evaluation function is reduced until obtaining the curved surface for meeting design requirement.Illumination optimization is usually required that pursues and attacks greatly in each Optimized Iterative
The light of amount is to reduce simulation statistical noise, and the result of optimization design is highly dependent on the selection of optimized variable, evaluation function
Building and optimization algorithm.The illumination complicated for one, it usually needs thousands of a discrete data points construct freedom
Curved surface, this is that optimization design cannot achieve.The design philosophy of PDE method is that the reverse engineer problem is converted to one one
Rank partial differential equations, and free form surface is constructed by numerical solution equation group.Compare optimization design, PDE method tool
There is higher design efficiency, and be able to achieve complicated lighting requirement, PDE method is all the research of Random Curved Surface Designing all the time
Emphasis.Chinese patent 200910046129.5 proposes a kind of design method for point light source light-distribution lens, this method according to
The law of refraction constructs the first order PDE system that curved surface is met, and selectes an energy topological relation then to determine light source
Energy mapping relations between target illumination, by numerical solution, the first order PDE system obtains free-curved-surface later
Type.A committed step using this kind of PDE method design free form surface is the energy that need to first establish between light source and target illumination
Measure mapping relations.The integrability of the energy mapping relations determines the continuity of free form surface, only meets the energy of integrability condition
Amount mapping relations can just obtain continuous free form surface.The energy mapping relations of some easy acquisitions are often unsatisfactory for that item can be accumulated
Part can only obtain discontinuous free form surface at this time.As Chinese patent 200910046129.5 uses a kind of variable separable
Mapping relations realize rectangular illumination, as a result can only obtain discontinuous free form surface, this is undoubtedly proposed to actual processing
Very big problem.Chinese patent 102928983 discloses a kind of for collimating the design of the freeform optics element of light shaping
Method, this method realize complicated illumination by the partial differential equation of second order of building curved surface face type, can obtain continuous freely bent
Face realizes the processable of curved surface.However, the above method is equal and element cannot achieve the target illumination with intensity singular point.
Summary of the invention
The design side that the purpose of the present invention is to provide a kind of suitable for preparing the freeform optics element of hollow beam
Method.Specific step is as follows:
(1) collimated light beam successively passes through freeform optics element and optical focusing system, according to initial design parameters pair
It carries out Random Curved Surface Designing；
(2) rectangular coordinate system, collimated light beam propagation side are established as coordinate plane xoy using a cross section of collimated light beam
To parallel with z-axis.To any point P on the free form surface designed needed for freeform optics element determined by step (1)
Coordinate be expressed as P (x, y, z (x, y)) with rectangular co-ordinate, the coordinate of target point T corresponding with point P is with straight on target illumination face
Angular coordinate is expressed as T (tx,ty,tz)；Vector P is the position vector of point P, is the vector that point P is directed toward by origin, and vector T is
The position vector of point T is the vector that point T is directed toward by origin；It is assumed that vector I indicates the unit direction vector of incident beam,
Vector O (Ox, Oy, Oz) indicates the direction vector of outgoing beam, and vector N indicates per unit system arrow of the curved surface at P point, by focusing
The optical characteristics of lens it is found thatWherein f is the focal length of condenser lens.
According to law of refraction noO=niI+P1N is obtained
WhereinzxAnd zyIt is z respectively about x and y
First-order partial derivative,niAnd noThe respectively refractive index of freeform optics element material therefor
With the refractive index of freeform optics component ambient medium；
(3) according to law of conservation of energy, establish light source outgoing luminous energy and target illumination field between received luminous energy
Energy relationship, in the case where not considering energy loss, it is desirable that the received light source emanated energy of freeform optics elements institute with
The energy for reaching target illumination field is equal, i.e., energy meets relational expression
Wherein, I (x, y) is intensity distribution of the collimated light beam in cross section, E (tx,ty) it is target illumination area on illuminated area
The Illumination Distribution in domain, S1And S2Respectively indicate the illumination region on the cross section and target face of collimated light beam；
(4) according to the coordinate relationship between step (2) obtained point P and target point T, there is following coordinate conversion relation
dtxdty=| J (T) | dxdy
Wherein, J (T) is the Jacobi matrix of position vector T,
(5) coordinate conversion relation in step (4) is substituted into the energy equation of step (3) and removes the sign of integration, retouched
The energy transmission equation of freeform optics element is stated, is after abbreviation
A1(zxxzyy-zxy 2)-I(x,y)/E(tx,ty)=0
Wherein, xmin≤x≤xmax, xminAnd xmaxThe respectively minimum value and maximum value of x value； ymin≤y≤ymax, ymin
And ymaxThe respectively minimum value and maximum value of y value；A1It is about zx,zyFunction.
(6) free form surface will also guarantee the boundary of light source outgoing while meeting the energy transmission equation in step (5)
Light is incident on the boundary of target face illumination region after free form surface deviation.
For the outer boundary of target area, using natural boundary conditions, to the light on any incident area outer boundary, warp
After free form surface deviation, drop point is located at target area outer boundary, it may be assumed that
Wherein, Ω1And Ω2The respectively cross section and target illumination field of incident laser beam；WithRespectively
Ω1And Ω2Outer boundary；
It is zero since target illumination field is center intensity, for the inner boundary of target area, controls in incident laser
Drop point light drop point of the heart light in different directions θ ∈ (0,2 π) meets:
Wherein,For Ω2Outer boundary.θ is emergent ray of the light central ray after deviation in xy plane
The angle of projection and x-axis
(7) it to the energy transmission equation in step (5) and the boundary condition simultaneous solution in (6), obtains on free form surface
One group of discrete data point, by the data point carry out surface fitting FREEFORM SURFACE MODEL can be obtained.
Compared with the prior art, the invention has the beneficial effects that:
1) the freeform optics element proposed by the present invention for being used to prepare hollow beam solves existing hollow beam system
The problem that capacity usage ratio is low, damage threshold is low in standby technology；
2) the freeform optics element proposed by the present invention for being used to prepare hollow beam solves existing hollow beam system
Not the problem of not being suitable for Gauss incident beam in standby technology；
3) the freeform optics element proposed by the present invention for being used to prepare hollow beam solves existing hollow beam system
The problem of hollow size and bright ring intensity can not be controlled quantitatively in standby technology；
4) the freeform optics element proposed by the present invention for being used to prepare hollow beam solves existing hollow beam system
There are problems that useless secondary lobe in target beam in standby technology；
5) the perfect freedom of the design method of the freeform optics element proposed by the present invention for being used to prepare hollow beam
The partial differential equation of second order design method of curved design solves the problems, such as the processing of boundary condition in intensity singular point beam shaping；
Detailed description of the invention
Fig. 1 is the optical system based on freeform optics element for being used to prepare hollow beam；
Fig. 2 is ideal medium altitude target illumination figure；
Fig. 3 is value discrete region schematic diagram；
Fig. 4 (a) is the freeform optics component models sectional view for being used to prepare hollow beam；
Fig. 4 (b) is the freeform optics component models perspective view for being used to prepare hollow beam；
Fig. 5 is the illumination spot in embodiment on target illumination face.
Specific embodiment
To keep the objectives, technical solutions, and advantages of the present invention clearer, the present invention is further illustrated with reference to the accompanying drawing.
Schematic diagram of optical system is as shown in Fig. 1, and collimated light beam successively passes through freeform optics element and optical focus
System obtains required Illumination Distribution in target face.Incident beam is collimation uniform beam, and free form surface is rectangular, long L=
2mm, wide W=2mm.Object illumination is the annular that a center intensity is zero, as shown in Fig. 2, Center Dark Spot radius r1=
0.05mm, outer diameter r2=0.75mm, uniform intensity distribution.It is established using a cross section of collimated light beam as coordinate plane xoy
Rectangular coordinate system, the collimated light beam direction of propagation are parallel with z-axis.The material of free-form surface lens is that refractive index is ni=1.4935
Polymethyl methacrylate PMMA, lens surrounding medium are air, that is, no=1, the focal length f=50mm of focusing system.
The unit direction vector I=(0,0,1) of incident ray, according to law of refraction noO=niI+P1N is obtained:
zxAnd zyIt is one of z about x and y respectively
Rank partial derivative,In conjunction with condenser lens to the convergence characteristic of light beam, point P and target point T is established
Between coordinate relationship
According to law of conservation of energy, the energy transmission equation of description freeform optics element is obtained, is after abbreviation
A1(zxxzyy-zxy 2)-I(x,y)/E(tx,ty)=0
Wherein,
For the outer boundary of target area, controls incident outer boundary light drop point and meets:
Wherein,
Ω1=(x, y) |-L/2≤x≤L/2 ,-W/2≤y≤W/2 },
WithRespectively Ω1And Ω2Outer boundary；
It is zero since target illumination field is center intensity, for the inner boundary of target area, controls in incident laser
Drop point light drop point of the heart light in different directions θ ∈ (0,2 π) meets:
(tx 2+ty 2)=r1 2: (x, y)=(0,0)
Wherein, θ is the angle of projection and x-axis of emergent ray of the light central ray after deviation on x/y plane；r1
It is the radius of Center Dark Spot in target face.
After converting mathematical problem as described above for lighting problem, above-mentioned math equation must be solved, and usually
Its numerical solution can only be acquired.First to region Ω1Carry out discretization, Ω1={ (xi,yj)|xi=ih1,yj=jh2, i=0,
1 ..., m, j=0,1 ..., n } h1,h2For x, the discrete steps in the direction y, m, the discrete point number in the direction n x, y, i, j be from
Position of the scatterplot in row and column.Region after discrete is as shown in Figure 4.Later, energy transmission equation is substituted using difference scheme
With the local derviation item in boundary condition equation, wherein the difference scheme of boundary point, interior point and vertex therein is all in accordance with its coordinate bit
Set the corresponding required precision specific choice of feature and Random Curved Surface Designing.Thus a non-linear side is converted by partial differential equation
Journey group, and Newton Algorithm equation group is used, the series of discrete data point on free form surface can be obtained.It may be noted that
It is in inner boundary processing, to takeThat is the boundary condition equation of inner boundary can be written as:
When θ value difference, zx,zyDifference scheme needed for point it is also different, by taking first quartile as an example
The discrete data point of calculated two free form surfaces carries out 3D modeling, constructs free-form surface lens mould
Type, as shown in Fig. 4.Lens model brought into optical software is simulated, to 8,000,000 light of lens trace.Predeterminated target
Illuminated area meets at point (0,0,145) perpendicular to z-axis and with z-axis, illumination spot is obtained in target face, as shown in Fig. 5.It can be with
Find out, the hollow size of target hot spot, which meets, is expected, and uniform intensity distribution, the efficiency of light energy utilization is high, reaches design requirement.
Claims (6)
1. a kind of free-form surface lens face type design method that can be used for preparing hollow beam, it is characterised in that steps are as follows:
(1) collimated light beam successively passes through freeform optics element (100) and optical focusing system (200), according to initial designs
Parameter carries out Random Curved Surface Designing；
(2) cartesian coordinate system, the collimated light beam direction of propagation are established as coordinate plane xoy using a cross section of collimated light beam
It is parallel with z-axis；
To the coordinates table of any point P on the free form surface designed needed for freeform optics element determined by step (1)
It is shown as P (x, y, z (x, y)), the coordinate representation of target point T corresponding with point P is T (t on target illumination facex,ty,tz)；Vector P
It is the vector that point P is directed toward by origin for the position vector of point P, vector T is the position vector of point T, is one and is referred to by origin
To the vector of point T；It is assumed that vector I indicates that the unit direction vector of incident beam, vector O (Ox, Oy, Oz) indicate outgoing beam
Direction vector, vector N indicate curved surface at P point per unit system arrow, by the optical characteristics of condenser lens it is found thatWherein f is the focal length of condenser lens；
According to law of refraction noO=niI+P1N is obtainedWherein
zxAnd zyIt is first-order partial derivative of the z about x and y respectively,niAnd noRespectively free form surface
The refractive index of optical element material therefor and the refractive index of freeform optics component ambient medium；
(3) in the case where not considering energy loss, according to law of conservation of energy, by any one light pencil of light source outgoing
Energy is to maintain constant during by the freeform optics element deviation, i.e., energy meets relational expression
E(tx,ty)dtxdty=I (x, y) dxdy
Wherein, I (x, y) is intensity distribution of the collimated light beam in cross section, E (tx,ty) it is target illumination field on illuminated area
Illumination Distribution,
(4) according to the coordinate relationship between step (2) obtained point P and target point T, there is following coordinate conversion relation
dtxdty=| J (T) | dxdy
Wherein, J (T) is the Jacobi matrix of position vector T,
(5) formula for entrepreneurship that the coordinate conversion relation in step (4) is substituted into step (3) obtains description freeform optics
The energy transmission equation of element is after abbreviation
A1(zxxzyy-zxy 2)-I(x,y)/E(tx,ty)=0
Wherein, xmin≤x≤xmax, xminAnd xmaxThe respectively minimum value and maximum value of x value；ymin≤y≤ymax, yminAnd ymax
The respectively minimum value and maximum value of y value；A1It is about zx、zyFunction；
(6) free form surface will also guarantee the boundary rays of light source outgoing while meeting the energy transmission equation in step (5)
The boundary of target face illumination region is incident on after free form surface deviation；
For the outer boundary of target area, using natural boundary conditions, to the light on any incident area outer boundary, through freedom
After curved surface deviation, drop point is located at target area outer boundary, it may be assumed that
Wherein, Ω1And Ω2The respectively cross section and target illumination field of incident collimated light beams；WithRespectively Ω1With
Ω2Outer boundary；
Since the center intensity of target illumination field is zero, for the inner boundary of target area, the center light of incident laser is controlled
Drop point light drop point of the line in different directions θ ∈ (0,2 π) meets:
Wherein,For Ω2Inner boundary, θ be projection of emergent ray of the light central ray after deviation in xoy plane
With the angle of x-axis；
(7) it to the boundary condition simultaneous solution in the energy transmission equation and step (6) in step (5), obtains on free form surface
One group of discrete data point, by the data point carry out surface fitting free-form surface lens face type can be obtained.
2. design method according to claim 1, which is characterized in that the freeform optics element is refractive,
Front surface (S1) is plane, and rear surface (S2) is free form surface；Before free-form surface lens are placed on focusing system, light beam is through freedom
After curved surface deviation, then the convergence of line focus system, hollow hot spot is obtained in target face.
3. design method according to claim 1 or 2, it is characterised in that the freeform optics element (100) by
Front surface (S1), (S2) and side surface (S3) is constituted below；Front surface (S1) is plane, and rear surface (S2) is free form surface, side
Face (S3) is the plane of four splicings.
4. design method according to claim 1, which is characterized in that the focusing system is saturating by single or multiple spherical surfaces
Microscope group at.
5. design method according to claim 1 or 4, it is characterised in that the optical focusing system (200) is by least
One spherical lens composition；Laser beam images in infinity after free-form surface lens (100) deviation, then through collector lens group
(200) after acting on, outgoing beam images in the back focal plane of collector lens group (200).
6. design method according to claim 1, it is characterised in that the boundary condition equation of described step (6) inner boundary
Are as follows:
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Cited By (6)
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| CN109613699A (en) * | 2019-02-19 | 2019-04-12 | 中国科学院长春光学精密机械与物理研究所 | A kind of free form surface illumination system layout method based on target to optical device |
| CN111413704A (en) * | 2020-04-16 | 2020-07-14 | 中国科学院云南天文台 | Laser ranging system comprising free-form surface lens beam shaping structure |
| CN111443483A (en) * | 2020-04-24 | 2020-07-24 | 中国科学院云南天文台 | Design method of beam shaping structure based on free-form surface lens |
| CN111638599A (en) * | 2020-06-09 | 2020-09-08 | 孔令豹 | Design and 3D printing preparation method of optical lens |
| CN112363316A (en) * | 2020-12-15 | 2021-02-12 | 之江实验室 | Design method for shaping light beam of spherical air chamber pumping laser system |
| CN113325577A (en) * | 2021-06-15 | 2021-08-31 | 中国人民解放军军事科学院国防工程研究院 | Design method of free-form surface condenser for optical system of solar simulator |
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Cited By (8)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN109613699A (en) * | 2019-02-19 | 2019-04-12 | 中国科学院长春光学精密机械与物理研究所 | A kind of free form surface illumination system layout method based on target to optical device |
| CN111413704A (en) * | 2020-04-16 | 2020-07-14 | 中国科学院云南天文台 | Laser ranging system comprising free-form surface lens beam shaping structure |
| CN111443483A (en) * | 2020-04-24 | 2020-07-24 | 中国科学院云南天文台 | Design method of beam shaping structure based on free-form surface lens |
| CN111638599A (en) * | 2020-06-09 | 2020-09-08 | 孔令豹 | Design and 3D printing preparation method of optical lens |
| CN112363316A (en) * | 2020-12-15 | 2021-02-12 | 之江实验室 | Design method for shaping light beam of spherical air chamber pumping laser system |
| CN112363316B (en) * | 2020-12-15 | 2022-05-27 | 之江实验室 | Design method for shaping light beam of spherical air chamber pumping laser system |
| CN113325577A (en) * | 2021-06-15 | 2021-08-31 | 中国人民解放军军事科学院国防工程研究院 | Design method of free-form surface condenser for optical system of solar simulator |
| CN113325577B (en) * | 2021-06-15 | 2022-04-22 | 中国人民解放军军事科学院国防工程研究院 | Design method of free-form surface condenser for optical system of solar simulator |
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Application publication date: 20181211 |